Quiver Yangians and time-variable repsentations

I will talk about the simplest quiver Yangians (affine Yangians $\mathfrak{gl}_1, \mathfrak{gl}_2, \mathfrak{gl}_{1,1}$) and a special class of representations on the space of polynomials from the Schur-Jack family, the so-called representations on time-variables. Thanks to this representation, a connection is established between the affine Yangian $\mathfrak{gl}_1$ and quantum integrable systems and matrix models. I will also talk about recent advances in the construction of time-variable representations for more complicated affine Yangians $\mathfrak{gl}_2$ and $\mathfrak{gl}_{1,1}$ and the search for corresponding integrable systems.